The side that triggered the Civil War was the side that was in the wrong, so I'm not sure what truth you are pointing to there.
However, their rhetoric goes much further than that. Their rhetoric says that abortion is equivalent to murder, and thus justifies curtailing inalienable rights held by women.
The right of self-defense of others is something very close to universally accepted. If there were an equivalent number of five year old kids being aborted, we would not see milquetoast efforts like sit-ins and prayer vigils, actions with both little consequence and impact.
I believe Eric Rudolph believed abortion is murder. But all those people at prayer vigils, sit-ins, Red Rose Rescue, and pregnancy centers do not. They see it as something bad, but less than murder.
If a half million five year old kids are being murdered, you can't just go about your life and attend an annual March for Life protest. What kind of a person doesn't do more? This is systematic, legal, mass-scale child murder we're talking about.
By that argument, no abolitionist except for John Brown actually believed that chattel slavery was wrong. No suffragettes except the anarchists actually believed that women should have the right to vote. No blacks in the USA in the 1960s actually believed they were equal in dignity with their white brothers.
Non-violent responses to violent outrages are a very Christian approach to the problems of evil. That doesn't mean there's no suffering involved. Pro-life activists are regularly arrested, assaulted, battered, and insulted. Pro-life organizations spend millions of dollars (gifted in charity by hundreds of thousands of pro-life people) every year helping woman who find themselves in difficult positions choose life and give their children a better life after birth. Time and treasure poured out for a cause are a better measure of the importance of a cause that the total weight of bullets expended in overcoming the other side.